Robust adaptive beamforming for general-rank signal models

The performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal. Such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment, sources, or sensor array. This is especially true when the desired signal components are present in the beamformer "training" data snapshots because in this case, the adaptive array performance is very sensitive to array and model imperfections. The similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly, but the training sample size is small. We propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary-type mismatches of the desired signal array response. Our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank-one (point source) and higher rank (scattered source/fluctuating wavefront) desired signal models. The proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst-case performance optimization. Simple closed-form solutions to the considered robust adaptive beamforming problems are derived. Our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms, while, at the same time, offer a significantly improved robustness and faster convergence rates.     

A Novel Adaptive Beamformer Based on Semidefinite Programming (SDP) With Magnitude Response Constraints

A novel robust adaptive beamformer, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With new constraints on the magnitude response, the beamwidth and response ripple of the robust response region can be well controlled. Moreover, only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom (DOFs) of the adaptive beamformer are consumed. Consequently, the resultant beamformer has significant improvement on signal-to-interference-plus-noise ratio (SINR). An important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix. In this paper, a method utilizing the extended spectral factorization method is proposed to solve this problem. Simple implementation, flexible performance control as well as significant SINR enhancement support the practicability of the proposed method.     

Robust Adaptive Microphone Array with Mainlobe and Response Ripple Control

Many existing adaptive beamformers possess robustness against arbitrary array steering vector (ASV) mismatches within presumed uncertainty set. However, when the array facing a large steering direction error, their performance degrade significantly since the uncertainty in steering direction generally gives rise to an outstanding mismatch in ASV. In the applications of microphone array, large steering direction error is often unavoidable because of the motion of target speaker. Meanwhile, in addition to conventional adaptive beamformers, microphone array also requests a controlled frequency response to target signal. In this paper, we propose a new adaptive microphone array implemented in frequency domain with controlled mainlobe and frequency response. A compact ASV uncertainty set explicitly modelling steering direction error and the other arbitrary ASV errors is exploited to derive beamformer with robust constraints on array magnitude response. Numerical results show that the proposed microphone array not only produces large controlled robust response region and robust frequency response, but also achieves high performance in SINR enhancement.     

基于稀疏约束和SRV约束的宽带自适应波束形成

针对传统的宽带MVDR自适应波束形成中,抑制干扰的同时会抬高旁瓣电平,且过多的线性约束会导致波束输出的SINR性能下降的问题,提出了一种基于SRV约束和稀疏约束的低旁瓣、高增益宽带自适应波束形成方法.该方法在窄带MVDR自适应波束形成基础上,通过增加波束图稀疏约束来降低波束的旁瓣电平,同时利用空间响应偏差(SRV)约束将窄带算法推广到宽带MVDR 自适应波束形成中,极大地降低了算法的复杂度,改善了波束输出的SINR 性能.与传统方法相比,该方法在降低宽带波束的旁瓣电平的同时,还具有良好的干扰抑制效果.数值仿真实验验证了该方法的有效性.     

基于幅相线性约束的自适应和差波束形成方法研究

阵列雷达自适应和差波束单脉冲测角面临信号对消、训练样本有限、波束保形及零点约束困难等问题.针对上述问题,本文提出基于幅相线性约束的自适应和差波束形成方法.该方法通过增加对主瓣临近角度的幅相线性约束条件,有效的克服和波束信号对消的现象;通过引入相位约束条件,使得差波束的在主瓣方向逼近静态差波束,具有良好的稳健性.同时通过合理的设计幅相约束条件实现了单脉冲和差波束测角二维解耦合.仿真实验验证了本文方法的有效性.     

脉冲噪声环境中鲁棒的自适应波束形成方法

本文提出一种脉冲噪声环境中的自适应波束形成方法.方法假定噪声服从对称 α 稳定(S α S:Symmetric α -stable)分布,首先定义分数低阶阵列响应,然后根据最小方差无畸变响应波束形成器(MVDR)提出分数低阶最小方差无畸变响应波束形成器(FrMVDR).理论上证明了当阶数小于噪声特征指数的一半时,分数低阶阵列输出功率有界.计算机仿真实验证明了本文提出的FrMVDR波束形成器在高斯噪声和非高斯脉冲噪声环境中性能都优于MVDR和其他有关的基于分数低阶矩的波束形成器,是一种鲁棒的自适应波束形成器.     

Efficient implementation of robust adaptive beamforming based on worst-case performance optimisation

Traditional adaptive beamforming methods undergo serious performance degradation when a mismatch between the presumed and the actual array responses to the desired source occurs. Such a mismatch can be caused by desired look direction errors, distortion of antenna shape, scattering due to multipath, signal fading as well as other errors. This mismatch entails robust design of the adaptive beamforming methods. Here, the robust minimum variance distortionless response (MVDR) beamforming based on worst-case (WC) performance optimisation is efficiently implemented using a novel ad hoc adaptive technique. A new efficient implementation of the robust MVDR beamformer with a single WC constraint is developed. Additionally, the WC optimisation formulation is generalised to include multiple WC constraints which engender a robust linearly constrained minimum variance (LCMV) beamformer with multiple-beam WC (MBWC) constraints. Moreover, the developed LCMV beamformer with MBWC constraints is converted to a system of nonlinear equations and is efficiently solved using a Newton-like method. The first proposed implementation requires low computational complexity compared with the existing techniques. Furthermore, the weight vectors of the two developed adaptive beamformers are iteratively updated using iterative gradient minimisation algorithms which eliminate the estimation of the sample matrix inversion. Several scenarios including angle-of-incidence mismatch and multipath scattering with small and large angular spreads are simulated to study the robustness of the developed algorithms.     

PSO Assisted DD-ESB Beamforming with Robust Capabilities

This paper deals with adaptive array beamforming based on the decision-directed eigenspace-based (DD-ESB) technique with robust capabilities. It has been shown that DD-ESB adaptive beamformer demonstrates the advantages of better output signal-to-interference plus noise ratio performance and less sensitivity to pointing error over conventional ESB beamformers without any specific training bits. In conjugation with particle swam optimization assisted scheme to obtain more correct desired user’s transmitted bits from the output of the ESB, the more correct steering vector of the desired user can be reconstructed for DD-ESB adaptive beamforming in the presence of larger pointing error and relatively low interference-to-noise ratio. Computer simulations are provided to illustrate the effectiveness of the proposed approach.     

一种分解迭代二阶锥规划鲁棒自适应波束形成算法

为有效克服导向矢量大失配误差对自适应波束形成器的影响,该文提出了一种最差性能最优的分解迭代鲁棒自适应波束形成算法。该算法对非凸的幅度响应约束问题进行分解处理,将问题转化为迭代的二阶锥规划问题,从而可对鲁棒响应区的波束宽度和纹波水平进行自由控制,并可得到较高的输出信干噪比。此外,与现有大部分该类鲁棒波束形成方法相比,提出的算法直接对权矢量进行优化,无需使用谱分解算法,避免了阵列结构的限制,可适用于任意阵形。仿真结果验证了算法的正确性和有效性。     

基于Laguerre滤波器等价设计的IIR宽带波束形成

常规IIR宽带波束形成器可以获得比FIR宽带波束形成器更好的性能,但其需要多极点的自适应调整过程,存在稳定性无法保证,计算复杂度较高等问题.本文提出一种新的基于IIR滤波器的宽带波束形成算法.该算法基于高阶Laguerre宽带波束形成器,利用双线性变换和函数束方法设计相应的低阶等价IIR宽带波束形成器.仿真实验及理论分析表明,该方法无需常规IIR宽带波束形成器的多极点自适应调整过程,在保证算法稳定性的同时,减少了计算复杂度,并提高了输出信干噪比(SINR).     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

MIMO雷达稳健的发射波束形成算法

针对发射导向矢量存在未知误差的问题,该文提出了一种MIMO雷达稳健的发射波束形成算法(Robust Transmitting Beamforming, RTB)。该算法在稳健的接收波束形成算法的基础上,以最大化最差情况输出信干噪比为优化准则,对发射导向矢量误差做稳健的发射波束形成。RTB算法属于对角加载方法。仿真结果表明,相比于已有算法,RTB算法的稳健性更好、计算复杂度更低、收敛速度更快。     

Broadband beamforming using Laguerre filters

Space-time processing is a well-substantiated method for designing broadband beamformers. In the conventional Frost space-time beamformer, tapped delay line (TDL) filters are used in each branch of the array to create a wideband response for interference suppression. In this article a new space-time beamforming method is introduced in which Laguerre filters replace the traditional TDL filters in the Frost beamformer. The Laguerre filters are fundamentally IIR filters but with only one pole in their structure. Unlike other IIR-based space-time beamforming methods, the proposed method does not need an adaptive procedure for the pole adjustment and is inherently stable. Simulation results show superior performance of the proposed method compared to the Frost beamformer and comparable results against other IIR-based beamformers with much less computational complexity and guaranteed stability.     

Self-Calibration-Based Robust Near-Field Adaptive Beamforming for Microphone Arrays

Near-field beamforming using a microphone array has found many applications, such as sound acquisition in small rooms. However, robust near-field adaptive beamforming (NABF) against focal point errors has not been studied much in the literature until recently. In this brief, a robust near-field adaptive beamformer is proposed. The proposed method is developed by combining a new formulation of the point-constrained NABF and a self-calibration technique, in the presence of focal point uncertainties. The proposed method suffers from no loss in the degrees of freedom for interference rejection. Compared with conventional calibration-based adaptive beamformers, the proposed method has the advantage of not needing a noise-free calibration signal. Simulation results demonstrate that the performance of the proposed method is superior to that of the existing methods     

Adaptive Beamforming Using Frequency Invariant Uniform Concentric Circular Arrays

This paper proposes new adaptive beamforming algorithms for a class of uniform concentric circular arrays (UCCAs) having near-frequency invariant characteristics. The basic principle of the UCCA frequency invariant beamformer (FIB) is to transform the received signals to the phase mode representation and remove the frequency dependence of individual phase modes through the use of a digital beamforming or compensation network. As a result, the far field pattern of the array is electronic steerable and is approximately invariant over a wider range of frequencies than the uniform circular arrays (UCAs). The beampattern is governed by a small set of variable beamformer weights. Based on the minimum variance distortionless response (MVDR) and generalized sidelobe canceller (GSC) methods, new recursive adaptive beamforming algorithms for UCCA-FIB are proposed. In addition, robust versions of these adaptive beamforming algorithms for mitigating direction-of-arrival (DOA) and sensor position errors are developed. Simulation results show that the proposed adaptive UCCA-FIBs converge much faster and reach a considerable lower steady-state error than conventional broadband UCCA beamformers without using the compensation network. Since fewer variable multipliers are required in the proposed algorithms, it also leads to lower arithmetic complexity and faster tracking performance than conventional methods.     

Coherent interference suppression with complementally transformedadaptive beamformer

This paper proposes a beamforming scheme for suppressing coherent interference with an array of arbitrary geometry. The scheme first uses estimates of the source directions to construct a transformation, which removes the desired signal while retaining the coherent interference. Optimum beamforming is then performed on the transformed data containing only interference and noise to produce the maximum output signal-to-interference-plus-noise ratio (SINR). Analysis and numerical results demonstrate that the proposed complementally transformed beamformer significantly outperforms the conventional multiply constrained minimum variance (MCMV) beamformers     

基于半正定约束的最差性能最优通用信号模型稳健波束形成算法

针对通用信号模型下的稳健波束形成问题,提出了一种基于半正定约束的最差性能最优稳健自适应波束形成算法,通过对波束形成器进行建模和变换,得到了一种简单的稳健自适应波束形成器的表达式。对波束形成器进行求解,不仅得到了最优权矢量的近似闭式解,而且获得了一定的性能改善,并且该算法具有较低的计算复杂度。仿真结果表明了该算法的有效性和正确性。     

Uniform Concentric Circular Arrays With Frequency-Invariant Characteristics—Theory, Design, Adaptive Beamforming and DOA Estimation

This paper proposes a new digital beamformer for uniform concentric circular arrays (UCCAs) having nearly frequency-invariant (FI) characteristics. The basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming or compensation network. As a result, the far-field pattern of the array, which is governed by a set of variable beamformer weights, is electronically steerable, and it is approximately invariant over a wider range of frequencies than conventional uniform circular arrays (UCAs). This also makes it possible to design the compensation network and the beamformer weights separately. The design of the compensation network is formulated as a second order cone programming (SOCP) problem and is solved optimally for minimax criterion. By employing the beamspace approach using the outputs of a set of fixed UCCA frequency-invariant beamformers (FIBs), a new beamspace MUSIC algorithm is proposed for estimating the direction-of-arrivals (DOAs) of broadband sources. Since the beampatterns of the UCCA-FIB is approximately invariant with frequency and is governed by a small set of weights, a very efficient adaptive beamformer using the minimum variance beamforming (MVB) approach can be developed. Simulation results using broadband Gaussian and multisinusoidal inputs show that the proposed adaptive UCCA-FIB is numerically better conditioned than the conventional broadband tapped-delay-line-based adaptive beamformers, due to the FI property and significantly fewer numbers of adaptive parameters. Consequently, a higher output signal-to-inference-plus-noise ratio over the conventional tapped-delay-line approach is observed. The usefulness of the proposed UCCA-FIB in broadband DOA estimation is also verified by computer simulation     

A User Parameter-Free Robust Adaptive Beamformer Based on General Linear Combination in Tandem with Steering Vector Estimation

If there is a mismatch between the assumed steering vector (SV) and the real value, the performance of adaptive beamforming methods is degraded. When the signal SV is known exactly but the sample size is small, the performance degradation can also occur. The second kind of degradation is mainly due to the mismatch between the sample covariance matrix and the real one. Almost all existing robust adaptive beamformers are proposed to improve the robustness against these two types of mismatch. Indeed, most of them are user parameter dependent, and the user parameter-free robust beamformers are scarce. As one of the shrinkage methods, the general linear combination (GLC) based beamformer is a good user parameter-free robust beamformer. However, it is only suitable for the scenarios with low sample size and/or small SV mismatch. In this paper, we propose a new robust beamformer, and it is based on general linear combination in tandem with SV estimation (GLCSVE). The proposed approach is superior to GLC in two aspects. One is that the GLCSVE beamformer performs well not only with small but also with large sample size. The other is that the GLCSVE can effectively deal with a large range of SV mismatch. Moreover, the proposed GLCSVE approach is a user parameter-free robust beamformer, and is more suitable for application than the parameter dependent approaches. The idea of our method can also be used to enhance other shrinkage based beamformers.     

Robust Beamforming via Worst-Case SINR Maximization

Minimum variance beamforming, which uses a weight vector that maximizes the signal-to-interference-plus-noise ratio (SINR), is often sensitive to estimation error and uncertainty in the parameters, steering vector and covariance matrix. Robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem. In this paper, we consider robust beamforming via worst-case SINR maximization, that is, the problem of finding a weight vector that maximizes the worst-case SINR over the uncertainty model. We show that with a general convex uncertainty model, the worst-case SINR maximization problem can be solved by using convex optimization. In particular, when the uncertainty model can be represented by linear matrix inequalities, the worst-case SINR maximization problem can be solved via semidefinite programming. The convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model. We illustrate the method with a numerical example.